Permutation groups .degree() function misleads.

[jasongrout]

Both of the graphs below are the path graph on 3 vertices. The problem is that the first labeling returns a permutation group of degree 2, when it should be of degree 3.

sage: g=Graph('Bo')
sage: print g.automorphism_group().degree()
2
sage: h=Graph('Bg')
sage: print h.automorphism_group().degree()
3
sage: g.is_isomorphic(h)
True

Component: basic arithmetic

Issue created by migration from https://trac.sagemath.org/ticket/3404

[rlmill]

comment:1

Unfortunately, since permutation groups are (currently) simply wrappers for GAP permutation groups, the object itself carries no notion of what it acts on, only a cycle representation of its generators.

sage: g=Graph('Bo')
sage: G=g.automorphism_group()
sage: G.degree?
Type:		instancemethod
Base Class:	<type 'instancemethod'>
String Form:	<bound method PermutationGroup_generic.degree of Permutation Group with generators [(1,2)]>
Namespace:	Interactive
File:		/Users/rlmill/sage-3.0.2/local/lib/python2.5/site-packages/sage/groups/perm_gps/permgroup.py
Definition:	G.degree(self)
Docstring:
    
            Synonym for largest_moved_point().
    
            EXAMPLES:
                sage: G = PermutationGroup([[(1,2,3),(4,5)],[(3,4)]])
                sage: G.degree()
                5

However, you can do:

sage: g.automorphism_group(translation=True, orbits=True)
(Permutation Group with generators [(1,2)], {0: 3, 1: 1, 2: 2}, [[0], [1, 2]])

The second is telling you which vertex of the graph is thought of as which integer by the group (here GAP thinks of this as 3 fixed, 4 fixed, 5 fixed, ...) and the third are the actual orbits of all the vertices.

This is a problem in permutation groups, not graphs.

[mwhansen]

Description changed:

--- 
+++ 
@@ -1,4 +1,3 @@
-
 Both of the graphs below are the path graph on 3 vertices.  The problem is that the first labeling returns a permutation group of degree 2, when it should be of degree 3.
 
 ```

[mwhansen]

comment:3

This has been fixed.

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| Sage Version 4.0.1.rc1, Release Date: 2009-06-04                   |
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sage: sage: g=Graph('Bo')
sage: sage: print g.automorphism_group().degree()
3
sage: g.automorphism_group()
Permutation Group with generators [(1,2)]